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Which One of the Following is Not a Prime Number?

Prime numbers are a fascinating concept in mathematics. They are the building blocks of all numbers and have unique properties that make them stand out. However, not all numbers can be classified as prime. In this article, we will explore the concept of prime numbers and determine which one of the following is not a prime number.

Understanding Prime Numbers

Before we delve into the question at hand, let’s first understand what prime numbers are. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In simpler terms, it is a number that cannot be divided evenly by any other number except 1 and itself.

For example, the first few prime numbers are 2, 3, 5, 7, 11, and so on. These numbers are only divisible by 1 and themselves, making them unique in the world of mathematics.

The List of Numbers

Now, let’s take a look at the list of numbers and determine which one is not a prime number:

  • 15
  • 17
  • 19
  • 23

Analyzing the Numbers

To determine which number is not a prime number, we need to check if each number satisfies the definition of a prime number. Let’s analyze each number one by one:

Number 15

Number 15 can be divided evenly by 1, 3, 5, and 15. Since it has divisors other than 1 and itself, it is not a prime number.

Number 17

Number 17 can only be divided evenly by 1 and 17. It does not have any other divisors, making it a prime number.

Number 19

Number 19 can only be divided evenly by 1 and 19. It does not have any other divisors, making it a prime number.

Number 23

Number 23 can only be divided evenly by 1 and 23. It does not have any other divisors, making it a prime number.

The Answer

After analyzing each number, we can conclude that 15 is not a prime number. It has divisors other than 1 and itself, which violates the definition of a prime number.

Why is 15 Not a Prime Number?

Now that we have determined that 15 is not a prime number, let’s explore why it fails to meet the criteria:

15 can be divided evenly by 1, 3, 5, and 15. These divisors indicate that 15 has factors other than 1 and itself. In fact, 15 can be expressed as the product of 3 and 5, which are both prime numbers. This factorization further confirms that 15 is not a prime number.

Conclusion

In conclusion, prime numbers are unique and fascinating entities in mathematics. They are numbers that can only be divided evenly by 1 and themselves. After analyzing the list of numbers, we determined that 15 is not a prime number. It has divisors other than 1 and itself, making it fail the criteria of a prime number. Understanding prime numbers and their properties is essential in various mathematical applications and problem-solving scenarios.

Q&A

1. What is a prime number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. It cannot be divided evenly by any other number.

2. What are some examples of prime numbers?

Some examples of prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on.

3. How can we determine if a number is prime?

To determine if a number is prime, we need to check if it can only be divided evenly by 1 and itself. If it has any other divisors, it is not a prime number.

4. Can prime numbers be negative?

No, prime numbers are defined as natural numbers greater than 1. They cannot be negative or fractions.

5. Are there an infinite number of prime numbers?

Yes, there are an infinite number of prime numbers. This was proven by the ancient Greek mathematician Euclid over 2,000 years ago.

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